9514 1404 393
Answer:
32
Step-by-step explanation:
If coefficients are positive integers, then the polynomial cannot be higher degree than 3. 10^4 = 10,000, so even a coefficient of 1 will give too large a value. P(1) = 8 tells us that the sum of coefficients must be 8, so we cannot have a degree lower than 3.
The sum of digits in 2312 is 8, so it works out that the polynomial is ...
P(x) = 2x^3 +3x^2 +x +2 . . . . matches P(1) = 8 and P(10) = 2312
Then P(2) is ...
P(2) = ((2·2 +3)2 +1)2 +2
P(2) = 32
Answer:
a) 1/2
b) 1/n
c) 1/4
Step-by-step explanation:
a) For each permutation, either 1 precedes 2 or 2 precedes 1. For each permutation in which 1 precedes 2, we can swap 1 and 2 to obtain a permutation in which 2 preceds 1. Thus, half of the total permutations will involve in 1 preceding 2, hence, the probability for a permutation having 1 before 2 is 1/2.
c) If 2 is at the start of the permutation, then it is impossible for 1 to be before 2. If that is not the case, then 1 has a probability of 1/n-1 to be exactly in the position before 2. We can divide in 2 cases using the theorem of total probability,
P( 1 immediately preceds 2) = P (1 immediately precedes 2 | 2 is at position 1) * P(2 is at position 1) + P(1 immediately precedes 2 | 2 is not at position 1) * P(2 is not at position 1) = 0 * 1/n + (1/n-1)*(n-1/n) = 1/n.
d) We can divide the total of permutations in 4 different groups with equal cardinality:
- Those in which n precedes 1 and n-1 precedes 2
- those in which n precedes 1 and 2 precedes n-1
- those in which 1 precedes n and n-1 precedes 2
- those in which 1 precedes n and 2 precedes n-1
All this groups have equal cardinality because we can obtain any element from one group from another by making a permutations between 1 and n and/or 2 and n-1.
This means that the total amount of favourable cases (elements of the first group) are a quarter of the total, hence, the probability of the event is 1/4.
Answer:
21x^5−21x^2
Step-by-step explanation:
hope this helps
No they cross each other like a highway. You are on the underpass and your friend passes over you. As in, they are crossing a bridge & you are below them.
100 3/4 x 75 1/2
25 x 3 x 75 1/2. (Divided by 4 to 100 and 4 to get 25)
25 x 3 x 75 1/2 ( multiple everything on top)
5625/2 ( then divided normally)
2812.5 or 2812 1/2
